Nonequilibrium transport through a Josephson quantum dot

Abstract

We study the electronic current through a quantum dot coupled to two superconducting leads which is driven by either a voltage V or temperature ∆T bias. Finite biases beyond the linear response regime are considered. The local two-particle interaction U on the dot is treated using an approximation scheme within the functional renormalization group approach set up in KeldyshNambu-space with U being the small parameter. For V > 0 we compare our renormalization group enhanced results for the dc-component of the current to earlier weak coupling approaches such as the Hartree-Fock approximation and second order perturbation theory in U . We show that in parameter regimes in which finite bias driven multiple Andreev reflections prevail small |U | approaches become unreliable for interactions of appreciable strength. In the complementary regime the convergence of the current with respect to numerical parameters becomes an issue-but can eventually be achieved-and interaction effects turn out to be smaller then expected based on earlier results. For ∆T > 0 we find a surprising increase of the current as a function of the superconducting phase difference in the regime which at T = 0 becomes the π (doublet) phase.

Phase-dependent heat and charge transport through superconductor–quantum dot hybrids

“…[42] and [43] for recent reviews on experiments and theory, respectively. In particular, there are investigations of the Josephson effect through quantum dots [44][45][46][47][48][49], multiple Andreev reflections [50][51][52][53][54][55], the interplay between superconducting correlations and the Kondo effect [56][57][58][59][60][61], the generation of unconventional superconducting correlations in quantum dots [62][63][64][65], Cooper pair splitting [66][67][68][69][70][71] and the generation of Majorana fermions [72][73][74][75]. Thermoelectric effects in superconductor-quantum dot hybrids have been studied in the absence of Coulomb interactions [76].…”

Functional renormalization group in Floquet space

“…Aiming at the long time behavior, we set t 0 to −∞, which allows to apply the following transformation to Floquet space. 33,35,45 The second time argument of the general Green's functions for X = ret, adv, K, <, > is Fourier transformed, 44…”

Local magnetic moments and electronic transport in closed loop quantum dot systems: A case of quadruple quantum dot ring at and away from equilibrium

“…Among other methods, the non-equilibrium fRG approach has some advantages: it does not require significant computational resources and results of its implementation are consistent with the ones obtained through more elaborate methods deal with non-equilibrium situations [56]. Recently, this method has been successfully applied to several quantum dot systems [56][57][58][59][60] and the comparative study to other numerical and semianalytical methods has been done [56,61]. Its application to systems with closed loop geometries formed by quantum dots was not however performed so far.…”